How do you create mask and "give it a diffuse shader" in this tutorial?
I guess you are confusing some concepts here.
You CANNOT combine the results you "save" in different render slots in the composite. (Unless you save them to a file and import them later on. But that's not what you want to do here.)
These Slots are mostly for comparing versions/settings of your render.

What you want to do, however, is add another render layer. (look at the right in your screenshot.) Use the [+]-Button to add a new render layer. You need separate layers for the planet and the atmosphere.

You should have something like this:





In this example, the first layer contains the Planet and the second contains the Atmosphere.

If you render this, that's what you'll see in the compositor:



THEN you can combine the results in Compositing.

HERE you can read more on render layers in Blender.

Hope this helps!

EDIT (answering the additional part of your question)

1)

To get more outputs from the first node, you need to select more render Passes for the render Layer, like so:



Here I selected all of them, just to show you.
However, to get the node, as seen in the Screenshot, just select "Emission".

The rest seems to be unnecessary. But I selected them as well, just to show you. (Note: Z = Depth in the current version of Blender) 



2)

Those are Glare Nodes, set to "Fog Glow":



2a) The Add Nodes are NOT math nodes! - These are Color Mix nodes. Get them here:



You can click on the top right icon of the node to toggle the preview.

3) This node is a Lens Distortion

Find it here: